WASHINGTON—The White House cautiously explored Tuesday new diplomatic options for handling the crisis in Syria, while President Barack Obama urged lawmakers to postpone voting on military strikes until the U.S. could size up a Russian-backed proposal for Syria to hand over its chemical weapons.

Sharp differences separated Russia and the U.S. and its allies over how the chemical-weapons issue should be resolved. France is proposing a resolution to the United Nations Security Council aimed at forcing Syria to give international inspectors full access to its chemical stockpile and allow for its swift dismantlement.

Russia called that resolution "unacceptable," citing the French proposal's use of Chapter 7, which would potentially authorize the use of force, as well as language that laid blame for using chemical weapons on the Syrian government. Russia said it would instead propose a draft declaration backing an initiative to put Syria's chemical weapons under international control.

A White House official said Mr. Obama spoke separately with France's President François Holland and U.K. Prime Minister David Cameron. The official said they agreed to work "closely together, and in consultation with Russia and China, to explore seriously the viability of the Russian proposal."

For its part, Syria said it would cease production of chemical weapons and disclose the locations of its stockpiles to the U.N., Russia and others, according to Russian media reports.

The State Department said Secretary of State John Kerry will travel to Geneva on Thursday to discuss Russia's proposal with Foreign Minister Sergei Lavrov. The two diplomats have held extensive discussions in recent months to devise ways to dismantle Damascus's chemical-weapons arsenal, said U.S. officials.

President Obama agreed to explore a Russian-backed proposal that would have Syria hand over its chemical weapons, while senators worked on new legislation to authorize a strike but provide time for a diplomatic alternative. Justin Vogt, senior editor at Foreign Affairs, joins the News Hub to discuss.

Mr. Kerry, speaking Tuesday with the public on a Google Inc. chat, expressed skepticism that the Obama administration would back a U.N. resolution that didn't include language to potentially authorize the use of force.

"We need a full resolution from the security-council order to have the confidence that this has the force that it ought to have," Mr. Kerry said. He also said that any resolution needed to "have consequences if games are played or if somebody tries to undermine this."

Mr. Kerry, in earlier testimony to the House Armed Services Committee, also urged lawmakers to back the administration's call to launch a limited attack against Syria if a last-minute diplomatic gambit fails, saying the talks have to quickly result in a genuine proposal that meets U.S. conditions.

"It has to be swift, it has to be real, it has to be verifiable," he said. "It cannot be a delaying tactic."

The fast-moving developments on the diplomatic front came as Mr. Obama met Tuesday afternoon with Senate Democrats and Republicans, and ahead of his planned prime-time speech Tuesday night.

A deal for Syria to turn over its chemical arsenal would pull the U.S. back from the brink of airstrikes on Syria. Talk of a possible diplomatic deal also altered the dynamic in Congress, where Mr. Obama has struggled to get backing for an authorization on use of force.

The Democratic meeting started with lawmakers watching videos of the alleged chemical-weapons attacks, according to Senate Majority Leader Harry Reid (D., Nev.). It created the "right setting" for the discussion, he said.

Sen. Dick Durbin (D., Ill.) said the president asked senators to give him time to determine whether the Russian proposal would work. "He needs a number of days," said Mr. Durbin. "The president was not overly optimistic about it."

Mr. Reid said it wasn't clear when a Senate vote on a resolution would be held, but that the timing will be dictated by international "developments taking place, not some artificial timeline."

After the Republican meeting, Sen. Ron Johnson (R., Wis.), who had voted against the use-of-force resolution that passed the Senate Foreign Relations Committee last week, said that "what the president asked us—and I totally agree with this—is we need to maintain a credible threat. We don't want to do anything to undermine that threat; I think it's moving us in the right direction." He added: "I've always said I'm going to keep an open mind."

Meanwhile, a bipartisan group of lawmakers was working to craft a new resolution that would call for the U.N. to pass a measure declaring that Syria had used chemical weapons and to remove them by a certain date. The date was still being negotiated but if the weapons aren't removed by that deadline, the resolution would authorize the president to launch limited military action.

"This is a way of both keeping the pressure on Syria and on Russia to get rid of the chemical weapons, which is the goal of this whole effort, but secondly, if they fail, then it would keep the authority to launch a strike," Sen. Carl Levin (D., Mich.), one of the lawmakers working on the measure, told reporters Tuesday.

Mr. Kerry set off the diplomatic scramble Monday when he suggested that President Bashar al-Assad could avert an attack by promptly handing over his chemical weapons to the international community. Russia, a close ally of Syria, quickly declared its support for such a plan and on Tuesday Syria said it would relinquish control of its chemical-weapon stockpiles.

The news of a possible diplomatic breakthrough drew mixed reactions elsewhere on Capitol Hill. House Speaker John Boehner (R., Ohio), who has backed using force in Syria, said he would prefer a diplomatic resolution to the crisis in Syria, but voiced doubts over the proposal.

"Diplomacy is always a better outcome than military action, but I will say I am somewhat skeptical of those that are involved in the diplomatic discussions today," Mr. Boehner said. "I'm skeptical of it because of the actors involved," referring to Russia and Syria.

House Minority Leader Nancy Pelosi (D., Calif.) said that if the Russian plan "isn't real, and the military sees an opportunity that is ideal," she would recommend that Mr. Obama "go forward" with a military strike. "We'll have time to discuss all the rest of it, but go forward because I don't believe that he needs the authorization," Mrs. Pelosi said.

Rep. Barbara Lee (D., Calif.), who has long been opposed to a military strike, said she was "cautiously optimistic" about Russia's proposal. She said she is also introducing an alternative that would include Russia's proposal for international control of Syria's chemical stockpiles as well as going to the U.N. General Assembly to get some action from the International Criminal Court.

"There are a variety of alternatives to military strikes that would lead to the same place," she said.

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